Implementation of OSPOP, an algorithm for the estimation of optimal sampling times in pharmacokinetics by the ED, EID and API criteria.

The most common approach to optimize the sampling schedule in parameter estimation experiments is the D-optimality criterion, which consists in maximizing the determinant of the Fisher information matrix (max det F). In order to incorporate prior parameter uncertainty in the optimal design, other criteria have been proposed: The ED = max E (det F), EID = min E (l/det F) and API = max E (log det F) criteria, where the expectation is with respect to the given prior distribution of the parameters. Previously described algorithm for the estimation of optimal sampling times according to these criteria are adaptive random search (ARS), a robust and global but slow optimizer for API, and stochastic gradient (SG), a fast but local optimizer for ED and EID. We implemented an algorithm named OSPOP 1.0, based on non-adaptive random search (RS) followed by stochastic gradient to determine optimal sampling times for parameter estimation in various pharmacokinetic models according to ED, EID and API criteria. Prior distributions are allowed to be uniform, normal or lognormal. This algorithm combines the robustness of RS and the speediness of SG (convergence is obtained in a few minutes on a microcomputer). The results of the SG algorithm have been compared to those described in the literature using the ARS algorithm on a one compartment model with first- order absorption and were very similar. Also, the CPU time needed by SG and ARS algorithms were compared and the former proved to be much faster. Then, it has been applied to a five parameters stochastic model with zero-order absorption rate and Weibull-distributed residence times which was shown to describe adequately the kinetics of metacycline in humans. Population pharmacokinetic parameters of metacycline were estimated from a six subject pilot study, by the iterative two-staged method, using ADAPT II repeatedly. Optimal sampling times were determined with each criterion (ED, EID, API) with a multivariate normal prior parameter distribution. Six to seven distinct sampling times could be estimated. Higher numbers of samples revealed coalescing of design points.